RS Aggarwal solution class 8 chapter 1 Rational Numbers Exercise 1F

Exercise 1F

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Q1 | Ex-1F | Class 8 | Rational Numbers | RS AGGARWAL | Chapter 1  | myhelper

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Question 1:

Find a rational number between $\frac{1}{4} \mathrm{and} \frac{1}{3}.$

Answer 1:

$$\begin{gathered} \mathrm{Required} \mathrm{number}=\frac{1}{2}(\frac{1}{4}+\frac{1}{3}) \\ =\frac{1}{2}\left(\frac{3+4}{12}\right) \\ =(\frac{1}{2}\times \frac{7}{12}) \\ =\frac{7}{24} \end{gathered}$$

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Q2 | Ex-1F | Class 8 | Rational Numbers | RS AGGARWAL | Chapter 1 | myhelper

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Question 2:

Find a rational number between 2 and 3.

Answer 2:

$$\begin{gathered} \mathrm{Required} \mathrm{Number}=\frac{1}{2}\times (2+3) \\ =\frac{5}{2} \end{gathered}$$

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Q3 | Ex-1F | Class 8 | Rational Numbers | RS AGGARWAL | Chapter 1 | myhelper

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Question 3:

Find a rational number between $\frac{-1}{3} \mathrm{and} \frac{1}{2}.$

Answer 3:

$$\begin{gathered} \mathrm{Required} \mathrm{number}=\frac{1}{2}\times \left(\frac{-1}{3}+\frac{1}{2}\right) \\ =\frac{1}{2}\times \left(\frac{-2+3}{6}\right) \\ =\frac{1}{2}\times \frac{1}{6} \\ =\frac{1}{12} \end{gathered}$$

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Q4 | Ex-1F | Class 8 | Rational Numbers | RS AGGARWAL | Chapter 1 | myhelper

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Question 4:

Find two rational numbers between −3 and −2.

Answer 4:

Required number$=\frac{1}{2} \times(-3-2)$
$=\frac{1}{2}(-5)=\frac{-5}{2}$

We know:$-3<\frac{-5}{2}<-2$

Rational number between -3 and $\frac{-5}{2}=\frac{1}{2} \times\left(-3-\frac{5}{2}\right)$
$=\frac{1}{2}\left(\frac{-6-5}{2}\right)$
$=\frac{1}{2} \times \frac{-11}{2}$
$=\frac{-11}{4}$

Thus, the required numbers are $\frac{-5}{2}$ and $\frac{-11}{4}$

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Q5 | Ex-1F | Class 8 | Rational Numbers | RS AGGARWAL | Chapter 1 | myhelper

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Question 5:

Find three rational numbers between 4 and 5.

Answer 5:

$$\begin{gathered} \mathrm{Rational} \mathrm{number} \mathrm{between} 4 \mathrm{and} 5: \\ \frac{1}{2}(4+5) \\ =\frac{9}{2} \\ \mathrm{Rational} \mathrm{number} \mathrm{between} 4 \mathrm{and} \frac{9}{2}: \\ \frac{1}{2}(4+\frac{9}{2}) \\ =\frac{1}{2}\left(\frac{8+9}{2}\right) \\ =\frac{1}{2}\left(\frac{17}{2}\right) \\ =\frac{17}{4} \\ \mathrm{Rational} \mathrm{number} \mathrm{between} \frac{9}{2}\mathrm{and} 5: \\ \frac{1}{2}(\frac{9}{2}+5) \\ =\frac{1}{2}\left(\frac{9+10}{2}\right) \\ =\frac{19}{4} \\ \mathrm{We} \mathrm{know}: \\ 4<\frac{17}{4}<\frac{9}{2}<\frac{19}{4}<5 \end{gathered}$$

$\mathrm{Thus}, \mathrm{the} \mathrm{three} \mathrm{rational} \mathrm{numbers} \mathrm{are}$$\frac{17}{4}, \frac{9}{2}$ and $\frac{19}{4}$.

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Q6 | Ex-1F | Class 8 | Rational Numbers | RS AGGARWAL | Chapter 1 | myhelper

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Question 6:

Find three rational numbers between $\frac{2}{3}$ and $\frac{3}{4}$.

Answer 6:

Rational number between $\frac{2}{3}$ and $\frac{3}{4}$:

$=\frac{1}{2}\left(\frac{2}{3}+\frac{3}{4}\right)$

$=\frac{1}{2}\left(\frac{8+9}{12}\right)$

$=\frac{17}{24}$

We know:
$\frac{2}{3}<\frac{17}{24}<\frac{3}{4}$


Rational number between $\frac{2}{3}$ and $\frac{17}{24}$:

$=\frac{1}{2}\left(\frac{2}{3}+\frac{17}{24}\right)$

$=\frac{1}{2}\left(\frac{16+17}{24}\right)$

$=\frac{1}{2}\left(\frac{33}{24}\right)$

$=\frac{33}{48}=\frac{33 \div 3}{48 \div 3}=\frac{11}{16}$


Rational number between $\frac{17}{24}$ and $\frac{3}{4}$:

$=\frac{1}{2}\left(\frac{17}{24}+\frac{3}{4}\right)$

$=\frac{1}{2}\left(\frac{17+18}{24}\right)$

$=\frac{1}{2}\left(\frac{35}{24}\right)$

$=\frac{35}{48}$

We know:
$\frac{2}{3}<\frac{11}{16}<\frac{17}{24}<\frac{35}{48}<\frac{3}{4}$
Thus, the three rational numbers are $\frac{11}{16}, \frac{17}{24}$ and $\frac{35}{48}$

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Q7 | Ex-1F | Class 8 | Rational Numbers | RS AGGARWAL | Chapter 1 | myhelper

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Question 7:

Find 10 rational numbers between $\frac{-3}{4} \mathrm{and} \frac{5}{6}.$

Answer 7:

LCM of 4 and 6 is 12.

Now,
$\frac{-3}{4}=\frac{-3 \times 3}{4 \times 3}=\frac{-9}{12}$ and $\frac{5}{6}=\frac{5 \times 2}{6 \times 2}=\frac{10}{12}$

Rational numbers lying between $\frac{-3}{4}$ and $\frac{5}{6}$ :

$\frac{-8}{12}, \frac{-7}{12}, \frac{-6}{12}, \frac{-5}{12}, \frac{-4}{12}, \ldots$ $\frac{1}{12}, \frac{2}{12}, \frac{3}{12}, \frac{4}{12}, \frac{5}{12}, \frac{6}{12}, \frac{7}{12}, \frac{8}{12}, \frac{9}{12}$

We can take any 10 out of these.

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Q8 | Ex-1F | Class 8 | Rational Numbers | RS AGGARWAL | Chapter 1 | myhelper

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Question 8:

Find 12 rational numbers between −1 and 2.

Answer 8:

We may write:
$-1=\frac{-10}{10}$ and $2=\frac{20}{10}$

Rational numbers between -1 and 2:-
$\frac{-9}{10}, \frac{-8}{10}, \frac{-7}{10}, \frac{-6}{10}, \frac{-5}{10}, \frac{-4}{10}, \ldots,$ $\frac{14}{10}, \frac{15}{10}, \frac{16}{10}, \frac{17}{10}, \frac{18}{10} \mathrm{and} \frac{19}{10}$
We can take any 12 numbers out of these.